Chemistry 12th Edition

Published by McGraw-Hill Education
ISBN 10: 0078021510
ISBN 13: 978-0-07802-151-0

Chapter 5 - Gases - Questions & Problems: 5.147

Answer

Please see the work below.

Work Step by Step

We can calculate the $v_{rms}$ for $N_2$ at room temperature as follows $v_{rms}=\sqrt{\frac{3RT}{M}}$ We plug in the known values to obtain: $v_{rms}=\sqrt{\frac{3(8.314\times 298)}{0.02802}}=515\frac{m}{s}$ We know that $v_{rms}(He)=\sqrt{\frac{3RT}{M}}$ We plug in the known values to obtain: $515=\sqrt{\frac{3(8.314)}{0.004003}}$ This simplifies to : $T=42.5665K$
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